Place the sliced peaches and sugar into a blender. Blend on high until the mixture is completely smooth and vibrant orange in color, about 30 seconds.
Pour the peach puree through a fine mesh sieve into a bowl to remove any remaining solids; press gently to extract mostly smooth juice.
Divide the strained peach nectar evenly between two flute glasses, filling each about halfway.
Slowly pour chilled Prosecco into each glass, tilting the glass gently to avoid too much foaming. Fill the glasses to the top with bubbles rising gently.
Gently stir the mixture with a stir stick or straw to combine the peach puree with the sparkling wine without losing too much carbonation.
Serve immediately while cold, garnished with a small peach slice or a sprig of fresh mint if desired. Enjoy the bubbly, fruity aroma and vibrant color.